Elliptic curve isogeny class 192.4-c over number field \(\Q(\sqrt{57}) \)

• Base field: \(\Q(\sqrt{57}) \)
• Label: 2.2.57.1-192.4-c
• Conductor: 192.4
• Rank: \( 1 \)

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 192.4-c over \(\Q(\sqrt{57}) \)

Isogeny class 192.4-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
192.4-c1	\( \bigl[a\) , \( 0\) , \( a\) , \( -37957 a - 124309\) , \( 684104 a + 2240382\bigr] \)
192.4-c2	\( \bigl[a\) , \( 0\) , \( a\) , \( -27372 a - 89644\) , \( 4737215 a + 15513985\bigr] \)